Environmental context explains Lévy and Brownian movement patterns of marine predators

An optimal search theory, the so-called Levy-flight foraging hypothesis(1), predicts that predators should adopt search strategies known as Levy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey(2-4). Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Levy behaviour has recently been questioned(5,6). Consequently, whether foragers exhibit Levy flights in the wild remains unclear. Crucially, moreover, it has not been tested whether observed movement patterns across natural landscapes having different expected resource distributions conform to the theory's central predictions. Here we use maximum-likelihood methods to test for Levy patterns in relation to environmental gradients in the largest animal movement data set assembled for this purpose. Strong support was found for Levy search patterns across 14 species of open-ocean predatory fish (sharks, tuna, billfish and ocean sunfish), with some individuals switching between Levy and Brownian movement as they traversed different habitat types. We tested the spatial occurrence of these two principal patterns and found Levy behaviour to be associated with less productive waters (sparser prey) and Brownian movements to be associated with productive shelf or convergence-front habitats (abundant prey). These results are consistent with the Levy-flight foraging hypothesis(1,7), supporting the contention(8,9) that organism search strategies naturally evolved in such a way that they exploit optimal Levy patterns.

A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling

1. A first step in the analysis of complex movement data often involves discretisation of the path into a series of step-lengths and turns, for example in the analysis of specialised random walks, such as Lévy flights. However, the identification of turning points, and therefore step-lengths, in a tortuous path is dependent on ad-hoc parameter choices. Consequently, studies testing for movement patterns in these data, such as Lévy flights, have generated debate. However, studies focusing on one-dimensional (1D) data, as in the vertical displacements of marine pelagic predators, where turning points can be identified unambiguously have provided strong support for Lévy flight movement patterns. 2. Here, we investigate how step-length distributions in 3D movement patterns would be interpreted by tags recording in 1D (i.e. depth) and demonstrate the dimensional symmetry previously shown mathematically for Lévy-flight movements. We test the veracity of this symmetry by simulating several measurement errors common in empirical datasets and find Lévy patterns and exponents to be robust to low-quality movement data. 3. We then consider exponential and composite Brownian random walks and show that these also project into 1D with sufficient symmetry to be clearly identifiable as such. 4. By extending the symmetry paradigm, we propose a new methodology for step-length identification in 2D or 3D movement data. The methodology is successfully demonstrated in a re-analysis of wandering albatross Global Positioning System (GPS) location data previously analysed using a complex methodology to determine bird-landing locations as turning points in a Lévy walk. For this high-resolution GPS data, we show that there is strong evidence for albatross foraging patterns approximated by truncated Lévy flights spanning over 3·5 orders of magnitude. 5. Our simple methodology and freely available software can be used with any 2D or 3D movement data at any scale or resolution and are robust to common empirical measurement errors. The method should find wide applicability in the field of movement ecology spanning the study of motile cells to humans.

Dynamics of air–sea CO2 fluxes in the northwestern European shelf based on voluntary observing ship and satellite observations

From January 2011 to December 2013, we constructed a comprehensive pCO2 data set based on voluntary observing ship (VOS) measurements in the western English Channel (WEC). We subsequently estimated surface pCO2 and air–sea CO2 fluxes in northwestern European continental shelf waters using multiple linear regressions (MLRs) from remotely sensed sea surface temperature (SST), chlorophyll a concentration (Chl a), wind speed (WND), photosynthetically active radiation (PAR) and modeled mixed layer depth (MLD). We developed specific MLRs for the seasonally stratified northern WEC (nWEC) and the permanently well-mixed southern WEC (sWEC) and calculated surface pCO2 with uncertainties of 17 and 16 μatm, respectively. We extrapolated the relationships obtained for the WEC based on the 2011–2013 data set (1) temporally over a decade and (2) spatially in the adjacent Celtic and Irish seas (CS and IS), two regions which exhibit hydrographical and biogeochemical characteristics similar to those of WEC waters. We validated these extrapolations with pCO2 data from the SOCAT and LDEO databases and obtained good agreement between modeled and observed data. On an annual scale, seasonally stratified systems acted as a sink of CO2 from the atmosphere of −0.6 ± 0.3, −0.9 ± 0.3 and −0.5 ± 0.3 mol C m−2 yr−1 in the northern Celtic Sea, southern Celtic sea and nWEC, respectively, whereas permanently well-mixed systems acted as source of CO2 to the atmosphere of 0.2 ± 0.2 and 0.3 ± 0.2 mol C m−2 yr−1 in the sWEC and IS, respectively. Air–sea CO2 fluxes showed important inter-annual variability resulting in significant differences in the intensity and/or direction of annual fluxes. We scaled the mean annual fluxes over these provinces for the last decade and obtained the first annual average uptake of −1.11 ± 0.32 Tg C yr−1 for this part of the northwestern European continental shelf. Our study showed that combining VOS data with satellite observations can be a powerful tool to estimate and extrapolate air–sea CO2 fluxes in sparsely sampled area.